Question

According to YouGov, 17% of Americans prefer chocolate ice cream over all other flavors. Supposeyou randomly select 300 Americans. What is the probability that exactly 50 of them preferchocolate ice cream? Round to the nearest ten-thousandth

Answer 1

Since we are asked to find the probability of an event ocurring exactly 50 times, we can use the binomial formula:

`P(X)=_nC_x\cdot p^x\cdot(1-p)^(n-x)`

where n is the number of trials, x is the number of successes and p is the probability of success on an individual trial.

`_nC_x=(n!)/(x!(n-x)!)`

With this fomula, let's use the data we were given:

`P(X)=_(300)C_(50)\cdot(0.17)^(50)\cdot(1-0.17)^(300-50)`
`P(X)=(300!)/(50!(250!))\cdot(0.17)^(50)\cdot0.83^(250)`

Using a calculator or a computer to do this operation, we get:

`P(X)\approx0.060969262`

And so, round to the neares ten thousandth:

`P(X)=0.0610`

or about 6.10%.